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Simplifying 3t3 + -30t2 + -21t = 0 Reorder the terms: -21t + -30t2 + 3t3 = 0 Solving -21t + -30t2 + 3t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3t'. 3t(-7 + -10t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-7 + -10t + t2)' equal to zero and attempt to solve: Simplifying -7 + -10t + t2 = 0 Solving -7 + -10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -10t + 7 + t2 = 0 + 7 Reorder the terms: -7 + 7 + -10t + t2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10t + t2 = 0 + 7 -10t + t2 = 0 + 7 Combine like terms: 0 + 7 = 7 -10t + t2 = 7 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 7 + 25 Reorder the terms: 25 + -10t + t2 = 7 + 25 Combine like terms: 7 + 25 = 32 25 + -10t + t2 = 32 Factor a perfect square on the left side: (t + -5)(t + -5) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (t + -5) equal to 5.656854249 and -5.656854249.Subproblem 1
t + -5 = 5.656854249 Simplifying t + -5 = 5.656854249 Reorder the terms: -5 + t = 5.656854249 Solving -5 + t = 5.656854249 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 5.656854249 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.656854249 + 5 t = 5.656854249 + 5 Combine like terms: 5.656854249 + 5 = 10.656854249 t = 10.656854249 Simplifying t = 10.656854249Subproblem 2
t + -5 = -5.656854249 Simplifying t + -5 = -5.656854249 Reorder the terms: -5 + t = -5.656854249 Solving -5 + t = -5.656854249 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -5.656854249 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.656854249 + 5 t = -5.656854249 + 5 Combine like terms: -5.656854249 + 5 = -0.656854249 t = -0.656854249 Simplifying t = -0.656854249Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.656854249, -0.656854249}Solution
t = {0, 10.656854249, -0.656854249}
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